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Classes of Submodular Constraints Expressible by Graph Cuts

  • Conference paper
Principles and Practice of Constraint Programming (CP 2008)

Part of the book series: Lecture Notes in Computer Science ((LNPSE,volume 5202))

Abstract

Submodular constraints play an important role both in theory and practice of valued constraint satisfaction problems (VCSPs). It has previously been shown, using results from the theory of combinatorial optimisation, that instances of VCSPs with submodular constraints can be minimised in polynomial time. However, the general algorithm is of order O(n 6) and hence rather impractical. In this paper, by using results from the theory of pseudo-Boolean optimisation, we identify several broad classes of submodular constraints over a Boolean domain which are expressible using binary submodular constraints, and hence can be minimised in cubic time. We also discuss the question of whether all submodular constraints of bounded arity over a Boolean domain are expressible using only binary submodular constraints, and can therefore be minimised efficiently.

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Authors and Affiliations

  1. Computing Laboratory, University of Oxford, Wolfson Building, Parks Road, Oxford, OX1 3QD, United Kingdom

    Stanislav Živný & Peter G. Jeavons

Authors
  1. Stanislav Živný
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  2. Peter G. Jeavons
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Peter J. Stuckey

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Živný, S., Jeavons, P.G. (2008). Classes of Submodular Constraints Expressible by Graph Cuts. In: Stuckey, P.J. (eds) Principles and Practice of Constraint Programming. CP 2008. Lecture Notes in Computer Science, vol 5202. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-85958-1_8

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  • DOI: https://doi.org/10.1007/978-3-540-85958-1_8

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-85957-4

  • Online ISBN: 978-3-540-85958-1

  • eBook Packages: Computer ScienceComputer Science (R0)

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